
In order to evaluate the Feynman parameter integral following our strategy in
Sec. REF , a factorization of
\(\left(\frac{x_1^2 v_{11}}{4}+\frac{x_1x_2v_{12}}{2}\right)^z\)  is required. Applying the
Binomi-Mellin-Newton integral
representation This integral representation does not have
a name in the literature
(see, e.g., Eq. (5.1) in Ref. [1]}, where it is just
referred to as a simple formula, however due to its frequent occurrence
and usefulness, it deserves, at least in the authors' opinion,
a name analogous to the well-established Cahen-Mellin integral.
As (REF ) is the Mellin integral
version of Newton's Binomial Theorem this name suggests itself.
\((a+b)^{z_1}=\frac{1}{\Gamma (-z_1)}\int _{-i\infty }^{i\infty }\frac{\mathrm {d}z_2}{2\pi i}a^{z_1-z_2} b^{z_2}\Gamma (-z_2)\Gamma (-z_1+z_2) \,,\) 
